RATIOS and

PROPORTIONS


Proportions and Fractions

Proportions expressed as Fractions are Solved by

Cross Multiplying.




Solving for X


(1) Set Up the fractions.


3

4
=
9

X



(2) Multiply the first numerator with the second

denominator and place it to the left of the equal sign.


3 • X
=



(3) Multiply the first denominator with the second

numerator and place it to the right of the equal sign.


3 • X
=
 4 • 9


3X
=
 36



(4) Solve for X by dividing the number opposite the equal

sign by the number on the same side as the equal sign.


X
=
 36 4


X
=
 9



(5) Prove the answer by replacing the letter with the number.


3

4
=
9

12


3 • 12
=
 4 • 9


36
=
 36





More Examples of Solving Fraction Proportions


7

5
=
14

X


7 • X
=
 5 • 14


7X
=
 70


X
=
 70 7


X
=
 10


7

5
=
14

10


7 • 10
=
 5 • 14


70
=
 70



* * * * *



1

20
=
X

100


1 • 100
=
 20 • X


100
=
 20X


100 20
=
 X


5
=
 X


1

20
=
5

100


1 • 100
=
 20 • 5


100
=
 100